how to set settings so recent snapshots don't go over HD icon?

I don't even know how to properly ask this question, so i'm sorry for any confusion.

Ok, before I sent my Macbook to the Genius repair, I could take snapshots and they would find their own space on the desktop. Now they go over the Macintosh HD icon. Same with whenever I insert a dvd, it goes over the HD icon. It's annoying because they all pile up on top of the HD icon.
Anyone know how to solve this? I would (and have) Google this if I knew the proper term for this. Please help.

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